The Bible is not a history book in that it’s purpose is not to record “Historical” data. It’s purpose it to present God’s Truth to people. It makes use of allegory to do so at times, but the message it’s conveying is still quite true.
For your examples from the OT:
Adam & Eve: The Church has not made a declarative statement about the literal historical truth of this account, so we are free to believe that it is allegory or fact. The purpose of the Genesis account is to relate a few things: #1: God created everything. Whether he did this it eh blink of an eye, or over the course of thirteen billion years is inconsequential. Everything that exists is through the will of God. #2: Through his will, he chose to create humanity, and give it sovereignty over his creation. Originally, humanity was clean, it knew no sin, and was in full communion with God. #3: The first humans (Adam and Eve) made a chose to reject God. We are not sure of the concrete form this choice took, it could have been eating the fruit, or it could have been something less tangible. The important thing is that a choice was made, and through that choice sin and spiritual death entered the world.
Noah: There is a great deal of debate as to whether this is a literal world-wide flood, or a localized flood which would have encompassed -the world- to the writer. Keep in mind that, while scripture is divinely inspired, it wouldn’t do the people of the time much good if it wasn’t written in a way they could understand. (this same logic could be used to explain a non-literal interpretation of the Genesis account. Ancient people wouldn’t have understood: "In the beginning there was a void, and within this void the Almighty created a singularity, encompassing all the matter that ever would be. From this singularity he brought forth the atoms which, after billions of years, coalesced into the elements. The first of these elements was Hydrogen, and from Hydrogen, fire was brought forth in the form of huge balls of burning plasma, and from this plasma was birthed the building blocks of the Earth, and all the life on it… etc… it’s much easier, and simpler, to say “And God said, let there be light” and it still conveys God’s power.) I don’t have much to say on Noah, it’s not something I’ve studied a lot, I’ll let someone else cover it.
Moses and the parting of the Red Sea: I see no issue with believing this one. While it doesn’t make complete scientific sense (the walls of eater on either side), God is not governed by science, science is governed by God. I don’t see why, accepting the reality of God’s existence and desire to guide humanity, you would have any trouble with this one
You also wrote about how, if the OT isn’t literal, how are we supposed to accept the NT? There is a distinct difference between the two. The OT developed with the Jewish civilization. It was originally an oral tradition, which was later submitted to paper. The methods of history conveyance were different at the time than during the writing of the NT. The gospels were pretty much written right after Christ’s death, by those who had walked with the Apostles as they spread the word of God, as were all of the NT books. The writing style of the gospels is the style used for Biography at the time, and the other books of the NT are mostly letters from the Apostles written to the different people of the world.
I hope other people will post and add to this, as I fear my explanation is woefully incomplete. If you are interested in the origin of the Bible, especially the NT, this is a fairly cheap book that goes over it:
Where we got the Bible
To recap briefly though, basically, the purpose of the OT was not to recount historical fact, but rather spiritual truth. They used various means to achieve this, part fact, and part allegory. The Church has put in a great deal of time studying the Scriptures, and have written extensively on the subject. My advice to you is to remember, “fact” is not the most important thing, it is Truth that you should be seeking.